You are now describing a layout with a disconnect on both sides of the fuse. While certainly possible, not so on my boat.
I'm describing what I believe is the prescribed ABYC wiring, which is:
- Battery,
- Fuse within 7" or I think a bit longer if the cable is sheathed,
- Battery disconnect switch.
Now you can start connecting loads, noting that there are a few exceptions for things you can fuse and directly connect to the battery.
Your inverter is a load and probably needs to be fused. There are two things that would trigger it. One would be if the wire to the inverter requires a fuse smaller than the battery fuse. The second would be if the inverter manufacturer call for it, which I think all do.
The disconnect part is optional, but is very convenient for service, especially if you don't want to shut down the whole DC system via the battery disconnect switch. You can use a breaker of some sort and get both in one package. Or you can use a fuse followed by a switch.
The reason for the fuse/switch order is that the wiring has a limit to how much current it can carry before you risk insulation breakdown and fire. The fuse is the limiting device, and needs to be at the beginning of the circuit, not midway through it.
Now I'm making an assumption here that may not be true, and that's that after the battery bank fuse and disconnect switch, you have some sort of DC power distribution point. It may be a simple terminal post, or a bus bar, or something more complex. Where power is drawn from that distribution point, it needs to be fused based on the circuit wire size. Now it's very possible that your boat doesn't have a battery disconnect switch, or battery fuse(s). I don't know when that became part of ABYC, or the degree to which various manufacturers follow those guidelines.